Nonaqueous secondary batteries comprising lithium can be expected to provide a high capacity and thus have been widely developed. In general, these lithium secondary batteries comprise a positive electrode and a negative electrode each comprising a material capable of reversibly intercalating and deintercalating a lithium, a nonaqueous electrolyte containing a lithium salt, and a separator. However, these prior art nonaqueous secondary batteries are disadvantageous in that if designed to accomplish their essential purposes, i.e., discharge at a high potential and secure a prolonged life and a high capacity, they exhibit a deteriorated preservability.